Solution:
Considering a fluid, of which $PVT$ behavior can be well predicted by the Redlich–Kwong–Soave Equation of State: $\displaystyle P = \frac{RT}{V – b} – \frac{a}{V \cdot (V + b)}$, where $b$ is a constant and $a$ is a temperature–dependent attracting term and a function of Pitzer acentric factor $\omega$.
\begin{parts}
\part [15] Please estimate the residual internal energy of this fluid, $U^R$, under an isotermal operation.
\part [5] If the parameter $a$ is specifically equal to $k \cdot T^{0.5}$, namely $\displaystyle a = \frac{k}{\sqrt{T}}$, where $k$ is a constant, please calculate the residual internal energy of this fluid, $U^R$, under an isothermal operation.
\end{parts}
